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    <div class="paper">
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        \[ n(r) = n_0 - \frac { n_2 \; r^2 } 2
          \;\;\;\;\;\;\;\;\;\;\;\;
          r^2 = x^2 + y^2
          \;\;\;\;\;\;\;\;\;\;\;\;
        \]
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            \[ n_2 > 0  \;\;\;\;\;\;\;\; \gamma = \sqrt \frac {n_2} {n_0} \]
            \[
            M\bigg\rvert_{n_2 > 0} = \begin{bmatrix}
                \cos(\gamma L) & \cfrac {\sin(\gamma L)} {n_0 \gamma} \\
                -n_0 \gamma \: \sin(\gamma L) & \cos(\gamma L) 
                \end{bmatrix}
            \]
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            \[ n_2 < 0 \;\;\;\;\;\;\;\; \gamma = \sqrt \frac {|n_2|} {n_0} \]
            \[
            M\bigg\rvert_{n_2 < 0} = \begin{bmatrix}
                \cosh(\gamma L) & \cfrac {\sinh(\gamma L)} {n_0 \gamma} \\
                n_0 \gamma \: \sinh(\gamma L) & \cosh(\gamma L) 
                \end{bmatrix}
            \]
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            \[
            M_{LF}\bigg\rvert_{n_2 > 0} = \begin{bmatrix}
                \cos(\gamma h) & \cfrac {\sin(\gamma h)} {n_0 \gamma} \\
                -\gamma \: \sin(\gamma h) & \cfrac {\cos(\gamma h)} {n_0} 
                \end{bmatrix}
            \]
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            \[
            M_{LF}\bigg\rvert_{n_2 < 0} = \begin{bmatrix}
                \cosh(\gamma h) & \cfrac { \sinh(\gamma h) } {n_0 \gamma} \\
                \gamma \: \sinh(\gamma h) & \cfrac {\cosh(\gamma h)} {n_0}
                \end{bmatrix}
            \]
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            \[
            M_{RT}\bigg\rvert_{n_2 > 0} = \begin{bmatrix}
                \cos(\gamma h) & \cfrac {\sin(\gamma h)} {\gamma} \\
                -n_0 \gamma \: \sin(\gamma h) & n_0 \cos(\gamma h) 
                \end{bmatrix}
            \]
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            \[
            M_{RT}\bigg\rvert_{n_2 < 0} = \begin{bmatrix}
                \cosh(\gamma h) & \cfrac {\sinh(\gamma h)} {\gamma} \\
                n_0 \gamma \: \sinh(\gamma h) & n_0 \cosh(\gamma h) 
                \end{bmatrix}
            \]
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